Publication number | US7349683 B2 |
Publication type | Grant |
Application number | US 10/999,191 |
Publication date | Mar 25, 2008 |
Filing date | Nov 30, 2004 |
Priority date | May 31, 2002 |
Fee status | Paid |
Also published as | CN1666112A, CN100473218C, EP1532465A1, US20050136944, WO2003102621A1 |
Publication number | 10999191, 999191, US 7349683 B2, US 7349683B2, US-B2-7349683, US7349683 B2, US7349683B2 |
Inventors | Pauli Misikangas, Petri Myllymäki |
Original Assignee | Ekahau Oy |
Export Citation | BiBTeX, EndNote, RefMan |
Patent Citations (6), Non-Patent Citations (2), Referenced by (35), Classifications (11), Legal Events (10) | |
External Links: USPTO, USPTO Assignment, Espacenet | |
This is a continuation of International Application No. PCT/FI03/00412, filed May 27, 2003, which claims priority from Finnish Application No. 20021043, filed May 31, 2002, the contents of both of which are incorporated herein by reference.
The invention relates generally to a positioning technique in which a target device's location is estimated on the basis of a sequence of observations on the target device's wireless communication environment.
More particularly, the invention relates to a positioning technique that is based on a hidden Markov model.
The locations along the target device's path can be called path points. The target device communicates via signals in a wireless environment, and signal values in the wireless environment are used for determining the target device's location.
A practical example of the target device is a data processing device communicating in a wireless local-area network (WLAN) or a cellular radio network. The data processing device may be a general-purpose laptop or palmtop computer or a communication device, or it may be a dedicated test or measurement apparatus such as a hospital instrument connected to the WLAN. A signal value, as used herein, is a measurable and location-dependent quantity of a fixed transmitter's signal. For example, signal strength and bit error rate/ratio are examples or measurable and location-dependent quantities.
The word ‘hidden’ in the hidden Markov model stems from the fact that we are primarily interested in the locations q_{t−2 }through q_{t+2 }but the locations are not directly observable. Instead we can make a series of observations o_{t−2 }through o_{t+2 }on the basis of the signal values but there is no simple relationship between the observations o_{t−2 }. . . o_{t+2 }and locations q_{t−2 }. . . q_{t+2}. (Note that the straight arrows through the locations q_{t−2 }through q_{t+2 }are not meant to imply that the target devices moves along a straight path or with a constant speed, or that the observations are made at equal intervals.)
A problem underlying the invention derives from the hidden Markov model: we cannot observe a variable that has a monotonous relationship with distance or location. Instead the positioning method is based on observations of signal values. It is possible for two or more locations to have near-identical sets of signal values, and a location estimate may be grossly inaccurate.
An object of the invention is to provide a method and an apparatus for implementing the method so as to alleviate the above disadvantages. In other words, it is an object of the invention to reduce the uncertainty of a positioning technique that is based on a probabilistic model of expected signal values. The object of the invention is achieved by the methods and equipment which are characterized by what is stated in the independent claims. The preferred embodiments of the invention are disclosed in the dependent claims.
The invention is based on the idea of using the target device's future observations to reduce the uncertainty concerning the target device's location. At first sight, this idea sounds absurd because at any given time, the target device's future observations are not known. Thus an apparent limitation of the invention is that it is only applicable to observations that do have at least one future. observation. In other words, the invention cannot directly reduce the uncertainty concerning the target device's most recent observation, but the invention is partially based on the surprising discovery that there are many applications that benefit from reducing the uncertainty concerning the target device's past observations. For example, the invention can be used to track customers' paths in a shop by attaching suitable target devices to shopping carts. Such information can be useful to design the placement of goods within the shop. Assume that a customer's path begins and ends at the points where the customer takes and leaves, respectively, the shopping cart. Thus the store owner is not interested in determining the most recent locations accurately because all paths end at the checkout points. On the other hand, the store owner is interested in determining the customers' paths inside the shop, and the most recent observations can be used to reduce the uncertainty concerning prior locations within the shop.
A method according to the invention comprises the following steps:
A sample point is a point of the probabilistic model, that is, a point for which signal value distributions are known either by calibration (physical measurements) or by simulations or theoretical calculations. Sample points may also be obtained by interpolation or extrapolation from other known locations.
Positioning accuracy can be further improved by making use of one or more past observations. The past and future observations are preferably combined by two-way recursion. This means that, if time is shown as advancing from left to right, past observations are taken into account by left-to-right (forward) recursion and future observations by right-to-left (backward) recursion.
If the invention is to be used in real-time positioning, a delay of at least one observation must be tolerated. To minimize the delay in real-time positioning, the number of future observations should be kept small. As used herein, real-time positioning means that the target device is positioned as soon as technically possible, even if there is a delay of one or a few observations.
In the following the invention will be described in greater detail by means of preferred embodiments with reference to the attached drawings, in which
A reference is again made to
It should also be understood that in
According to the invention, uncertainty concerning the target device's location q_{t }can be reduced by using not only the current observation o_{t }but one or more future observations o_{t+m}, where m is a positive integer. Two future observations o_{t+1 }and o_{t+2 }are denoted by arrows 34 and 35, respectively. Naturally, prior observations o_{t−2 }and o_{t−1 }can also be used to reduce positioning uncertainty, as shown by arrows 31 and 32, respectively.
The invention can be used to estimate the target device's location and/or its path. The two applications (location and path estimation) can be formally expressed as follows. In location estimation, we wish to maximize the probability of a single location given a sequence of observations. Formally stated, we wish to maximize p(q_{t}|O_{1} ^{T}). (Alternatively, we wish to determine a location having the smallest expected error; for instance location estimate may be a probability-weighted average of several locations.) In path estimation, we wish to maximize the probability of a path (a sequence of locations) given a sequence of observations. Formally stated, we wish to maximize p(q_{1} ^{T}|O_{1} ^{T}). (Alternatively, we may wish to determine a path having the smallest expected error.) The difference between the two applications is that in location estimation, each location is estimated separately (although based on a sequence of observations). Thus a path of consecutive locations may penetrate walls or be otherwise very unlikely, if that path is the one that maximizes the probabilities of individual locations. In path estimation, the most probable path is selected. Path estimation can be accomplished by determining transition probabilities between locations and determining the path that maximizes a combination of individual location probabilities and transition probabilities such that a most probable path is determined.
Note that
There is also a location calculation module LCM for producing a location estimate LE on the basis of the target device's observation set OS and the probabilistic model PM. For instance, the location calculation module can be implemented as a software program being executed in a laptop or palmtop computer. Technically, the ‘measurements’ and ‘observations’ can be performed similarly, but to avoid confusion, the term ‘measurement’ is generally used for the calibration measurements, and the signal parameters obtained at the current location of the target device are called ‘observations’. The target device's most recent set of observations is called current observations.
Note that
The example shown in
In the embodiment shown in
In the example shown in
Recursion-based techniques
Given a time-ordered sequence of observations o_{1} ^{T}={o_{1}, . . . , o_{T}} we want to determine the location distribution q_{t }at time t, 1≦t≦T. Assume that an observation o_{i }only depends on the current location q_{i }and that q_{i }only depends on the previous location q_{i−1}. The latter assumption means that history is not studied further than one prior observation. If these assumptions are met, we can represent the positioning problem as a hidden Markov model (HMM) of order 1 where o_{1} ^{T }is a sequence of observations and q_{1} ^{T }is a sequence of locations. In this case, the joint probability of o_{1} ^{T }and q_{1} ^{T }is:
P(o _{1} ^{T} ,q _{1} ^{T})=P(q _{1})Π_{t=1 . . . T−1} P(q _{t+1} |q _{t})Π_{t=1 . . . T} P(o _{t} |q _{t}) [1]
The joint distribution is therefore completely specified in terms of
If all locations are considered equally probable by default, we can simplify equation 1 by setting the initial state probability P(q_{1}) same for all locations. Thus, the joint distribution depends only on the transition probabilities and observation probabilities. These probabilities can be defined in various ways. For example, transition probabilities can be based on the spatial distance between locations so that the transition probability approaches zero when the distance increases. Because the invention can be applied regardless on how transition and observation probabilities are determined, we assume from now on that the transition probabilities and the observation probabilities are given.
The location distribution at time t can be defined as:
P(q _{t}|o_{1} ^{T})=P(o _{1} ^{t} ,q _{t})P(o _{t+1} ^{T} |q _{t})/P(o _{1} ^{T}) [2]
Herein P(o_{1} ^{t},q_{t}) and P(o_{t+1} ^{T}|q_{t}) are obtained from equations 3 and 4 (forward and backward recursions) and P(o_{1} ^{T}) is the probability of the observations, used for normalizing. Let S be the set of possible locations in this model and n=|S| be the size of S. The time complexity of the forward and backward recursions is O(Tm) where T is the length of the history and m is the number of non-zero transition probabilities at each time step. Obviously, m≦n^{2 }because in the worst case all transitions have non-zero probability. Most transitions have a probability of zero, however, so in practice m<<n^{2 }which makes computation very fast.
P(o _{1} ^{t} ,q _{t})=P(o _{t} |q _{t})Σ_{qt−1} P(q _{t} |q _{t−1}) P(o _{1} ^{t−t} ,q _{t−1}) [3]
P(o _{t+1} ^{T} |q _{t})=Σ_{qt+1} P(o _{t+1} |q _{t+1})P(q _{t+1} |q _{t})P(o _{t+2} ^{T} |q _{t+1}) [8]
In this way we can obtain the probabilities of different locations at a given time. However, many applications require a location estimate that is a single location instead of the location distribution. Again, there are several ways to calculate the point estimate at time t. For example, the point estimate can be a weighted average of locations where the location probability is used as the weight, or the location having the highest probability.
In order to find the most likely route, the Viterbi algorithm can be used. The Viterbi algorithm can find a sequence of locations s_{1}, . . . ,s_{T }that it maximizes the probability P(o_{1} ^{T}|q_{1}=s_{1}, . . . ,q_{T}=s_{T}). Obviously, a location s_{t }can be used as the location estimate at time t. However, this method has the drawback that at each time step, the location estimate can only be one of the possible locations. Thus, the accuracy of the location estimate depends on the density of possible locations. Accuracy could be improved by using large S having possible locations very close to each other. Unfortunately, this would radically increase time requirements of the algorithm.
In order to gain accurate location estimates with reasonable amount of computation, we can use relatively small S and calculate location estimate for time t as a weighted average of possible locations Σ(w_{i}·s_{i})/Σw_{i}. The weight w_{i }for a location s_{i }can be defined as the probability of the most likely path that goes through location s_{i }at time t. Path probabilities are obtained by using the Viterbi algorithm normally for time steps 1-t (creating forward paths) and backwards from time step T to t (creating backward paths) and multiplying the probabilities of forward and backward paths ending to s_{i }for each i=1 . . . n.
The following detailed calculations demonstrate how, at least in some situations, the invention can improve positioning accuracy even in real-time positioning. In some situations, the improvement may be significant. The following table 1 contains observation probabilities for locations A to F at (discrete) times t=1 to 5. Bold values show the observation probabilities of the real path A,B,D,E,F at each time step. Note that although the real location at time t=3 is D, location C has a higher observation probability. Hence, positioning based only on the current observation probabilities would fail at that point. Table 2 contains transition probabilities between locations A to F. Tables 3 to 5 contain. normalized calculation results for forward, backward. and two-way recursions (equations 3, 4 and 2), respectively. Again, probabilities of real locations at each time step are shown in bold text. Table 6 shows probabilities for locations A to F at time t=3.
TABLE 1 | ||||||
observation probabilities: | ||||||
t | A | B | C | D | E | F |
1 | 0.6 | 0.2 | 0.08 | 0.1 | 0.01 | 0.01 |
2 | 0.2 | 0.62 | 0.1 | 0.05 | 0.02 | 0.01 |
3 | 0.08 | 0.15 | 0.45 | 0.3 | 0.01 | 0.01 |
4 | 0.01 | 0.01 | 0.1 | 0.2 | 0.58 | 0.1 |
5 | 0.01 | 0.01 | 0.1 | 0.05 | 0.1 | 0.73 |
TABLE 2 | ||||||
transition probabilities | ||||||
To | ||||||
From | A | B | C | D | E | F |
A | 0.5 | 0.5 | 0 | 0 | 0 | 0 |
B | 0.2 | 0.4 | 0.2 | 0.2 | 0 | 0 |
C | 0 | 0.5 | 0.5 | 0 | 0 | 0 |
D | 0 | 0.3 | 0 | 0.4 | 0.3 | 0 |
E | 0 | 0 | 0 | 0.3 | 0.4 | 0.3 |
F | 0 | 0 | 0 | 0 | 0.5 | 0.5 |
TABLE 3 | ||||||
forward recursion: | ||||||
T | A | B | C | D | E | F |
1 | 0.6000 | 0.2000 | 0.0800 | 0.1000 | 0.0100 | 0.0100 |
2 | 0.1889 | 0.7750 | 0.0222 | 0.0115 | 0.0022 | 0.0002 |
3 | 0.0970 | 0.3056 | 0.3634 | 0.2337 | 0.0002 | 0.0000 |
4 | 0.0108 | 0.0417 | 0.2398 | 0.3054 | 0.4022 | 0.0001 |
5 | 0.0010 | 0.0165 | 0.0908 | 0.0889 | 0.1788 | 0.6239 |
TABLE 4 | ||||||
backward recursion: | ||||||
T | A | B | C | D | E | F |
1 | 0.1761 | 0.3818 | 0.1798 | 0.2156 | 0.0376 | 0.0090 |
2 | 0.0069 | 0.2892 | 0.0291 | 0.3573 | 0.2876 | 0.0300 |
3 | 0.0006 | 0.0202 | 0.0092 | 0.2584 | 0.4017 | 0.3099 |
4 | 0.0070 | 0.0740 | 0.0520 | 0.0520 | 0.4200 | 0.3950 |
5 | 0.1667 | 0.1667 | 0.1667 | 0.1667 | 0.1667 | 0.1667 |
TABLE 5 | ||||||
two-way recursion: | ||||||
T | A | B | C | D | E | F |
1 | 0.4838 | 0.3496 | 0.0659 | 0.0987 | 0.0017 | 0.0004 |
2 | 0.0056 | 0.9710 | 0.0028 | 0.0178 | 0.0027 | 0.0000 |
3 | 0.0008 | 0.0881 | 0.0476 | 0.8620 | 0.0012 | 0.0002 |
4 | 0.0004 | 0.0154 | 0.0622 | 0.0792 | 0.8426 | 0.0002 |
5 | 0.0010 | 0.0165 | 0.0908 | 0.0889 | 0.1788 | 0.6239 |
TABLE 6 | |||||
probabilities for locations A to F at time t = 3 | |||||
Location | Forward | Backward | Two-way | ||
A | 9.7% | 0.1% | 0.1% | ||
B | 30.6% | 2.0% | 8.8% | ||
C | 36.3% | 0.9% | 4.8% | ||
D | 23.4% | 25.8% | 86.2% | ||
E | 0.0% | 40.2% | 0.1% | ||
F | 0.0% | 31.0% | 0.0% | ||
In this example, after making five observations, the best estimate for the target's location at the time of the third observation is D. The probability for D being the correct location is 86 percent, which is shown in bold text in table 6. But neither the forward nor the backward recursion alone cannot determine that D is the most likely location. Forward recursion shows that C and B are more likely locations than D. while the backward recursion prefers locations E and F. The two-way recursion virtually eliminates false location estimates.
It is readily apparent to a person skilled in the art that, as the technology advances, the inventive concept can be implemented in various ways. The invention and its embodiments are not limited to the examples described above but may vary within the scope of the claims.
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U.S. Classification | 455/404.2, 455/456.1, 455/440 |
International Classification | H04L12/56, H04M11/04, H04W64/00, G01S5/02 |
Cooperative Classification | G01S5/0252, H04W64/00 |
European Classification | H04W64/00, G01S5/02D |
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